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56,219
Eigenvalues And Weights Of Induced Subgraphs
, 1999
"... We apply eigenvalue techniques for cut evaluation to produce relations between the weight and order of induced subgraphs, and apply these results to bound the stability number. ..."
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We apply eigenvalue techniques for cut evaluation to produce relations between the weight and order of induced subgraphs, and apply these results to bound the stability number.
A Semi-induced Subgraph . . .
- J. GRAPH THEORY 31 (1999), 29-49
, 1999
"... Let β(G) and Γ(G) be the independence number and the upper domination number of a graph G, respectively. A graph G is called Γ-perfect if β(H) = Γ(H), for every induced subgraph H of G. The class of Γ-perfect graphs generalizes such well-known classes of graphs as strongly perfect graphs, absorbant ..."
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Let β(G) and Γ(G) be the independence number and the upper domination number of a graph G, respectively. A graph G is called Γ-perfect if β(H) = Γ(H), for every induced subgraph H of G. The class of Γ-perfect graphs generalizes such well-known classes of graphs as strongly perfect graphs
Induced Subgraphs of Johnson Graphs
, 2006
"... The Johnson graph J(n, N) is defined as the graph whose vertices are the nsubsets of the set {1, 2, · · · , N}, where two vertices are adjacent if they share exactly n−1 elements. Unlike Johnson graphs, induced subgraphs of Johnson graphs (JIS for short) do not seem to have been studied before. W ..."
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The Johnson graph J(n, N) is defined as the graph whose vertices are the nsubsets of the set {1, 2, · · · , N}, where two vertices are adjacent if they share exactly n−1 elements. Unlike Johnson graphs, induced subgraphs of Johnson graphs (JIS for short) do not seem to have been studied before
Induced Subgraphs With Distinct Sizes
, 2009
"... We show that for every 0 <ɛ<1/2, there is an n0 = n0(ɛ) such that if n> n0 then every n-vertex graph G of size at least ɛ ( ) () n n and at most (1 − ɛ) contains induced k-vertex 2 2 subgraphs with at least 10−7k different sizes, for every k ≤ ɛn. This is best possible, up to a constant 3 ..."
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Cited by 1 (0 self)
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We show that for every 0 <ɛ<1/2, there is an n0 = n0(ɛ) such that if n> n0 then every n-vertex graph G of size at least ɛ ( ) () n n and at most (1 − ɛ) contains induced k-vertex 2 2 subgraphs with at least 10−7k different sizes, for every k ≤ ɛn. This is best possible, up to a constant
Detecting induced subgraphs
, 2007
"... An s-graph is a graph with two kinds of edges: subdivisible edges and real edges. A realisation of an s-graph B is any graph obtained by subdividing subdivisible edges of B into paths of arbitrary length (at least one). Given an s-graph B, we study the decision problem Î B whose instance is a graph ..."
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Cited by 11 (6 self)
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G and question is âDoes G contain a realisation of B as an induced subgraph?â. For several Bâs, the complexity of Î B is known and here we give the complexity for several more. Our NP-completeness proofs for Î Bâs rely on the NP-completeness proof of the following problem. Let S be a set
Line Graphs and Forbidden Induced Subgraphs
, 2001
"... Beineke and Robertson independently characterized line graphs in terms of nine forbidden induced subgraphs. In 1994, S8 oltes gave another characterization, which reduces the number of forbidden induced subgraphs to seven, with only five exceptional cases. A graph is said to be a dumbbell if it cons ..."
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Cited by 4 (1 self)
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Beineke and Robertson independently characterized line graphs in terms of nine forbidden induced subgraphs. In 1994, S8 oltes gave another characterization, which reduces the number of forbidden induced subgraphs to seven, with only five exceptional cases. A graph is said to be a dumbbell
Sizes of induced subgraphs of Ramsey graphs
, 2008
"... An n-vertex graph G is c-Ramsey if it contains neither a complete nor an empty induced subgraph of size greater than c log n. Erdős, Faudree and Sós conjectured that every c-Ramsey graph with n vertices contains Ω(n 5/2) induced subgraphs any two of which differ either in the number of vertices or i ..."
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Cited by 3 (1 self)
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An n-vertex graph G is c-Ramsey if it contains neither a complete nor an empty induced subgraph of size greater than c log n. Erdős, Faudree and Sós conjectured that every c-Ramsey graph with n vertices contains Ω(n 5/2) induced subgraphs any two of which differ either in the number of vertices
Results 1 - 10
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56,219
